Optical Engineering 46͑9͒, 093604 ͑September 2007͒ Evaluation of brilliance, fire, and scintillation in round brilliant gemstones Jose Sasian, FELLOW SPIE Abstract. We discuss several illumination effects in gemstones and University of Arizona present maps to evaluate them. The matrices and tilt views of these College of Optical Sciences maps permit one to find the stones that perform best in terms of illumi- 1630 East University Boulevard nation properties. By using the concepts of the main cutter’s line, and the Tucson, Arizona 85721 anti-cutter’s line, the problem of finding the best stones is reduced by E-mail: [email protected] one dimension in the cutter’s space. For the first time it is clearly shown why the Tolkowsky cut, and other cuts adjacent to it along the main cutter’s line, is one of the best round brilliant cuts. The maps we intro- Jason Quick duce are a valuable educational tool, provide a basis for gemstone grad- Jacob Sheffield ing, and are useful in the jewelry industry to assess gemstone American Gem Society Laboratories performance. © 2007 Society of Photo-Optical Instrumentation Engineers. 8917 West Sahara Avenue ͓DOI: 10.1117/1.2769018͔ Las Vegas, Nevada 89117 Subject terms: gemstone evaluation; gemstone grading; gemstone brilliance; gemstone fire; gemstone scintillation; gemstone cuts; round brilliant; gemstones; diamond cuts; diamonds. James Caudill American Gem Society Advanced Instruments Paper 060668R received Aug. 28, 2006; revised manuscript received Feb. 16, 8881 West Sahara Avenue 2007; accepted for publication Apr. 10, 2007; published online Oct. 1, 2007. Las Vegas, Nevada 89117 Peter Yantzer American Gem Society Laboratories 8917 West Sahara Avenue Las Vegas, Nevada 89117 1 Introduction are refracted out of the stone. Each beam generation carries Craftsmanship of gemstones that produce appealing illumi- less and less energy according to the Fresnel coefficients, to nation effects has been an endeavor of the gem cutting light absorption in the bulk of the gemstone material, or to industry throughout its history. Early gem cutters found that light scattering by material inclusions. Light that exits the by properly designing and cutting a gem, especially clear gemstone may reach the eyes of an observer creating a diamonds, it was possible to capture light from above the plurality of illumination effects that significantly impact the gem and redirect it to the eyes of an observer. Gems are appearance of the gemstone. Among the most important produced with a variety of cuts that comprise a plurality of and long-recognized1 effects are gem brilliance, gem fire, planar surfaces called facets. The top facets form the crown gem scintillation, and gem leakage. Historically there have and the bottom facets form the pavilion of the stone. The been several definitions of these effects that capture their facets themselves are polygonal in their boundary. Facets in essence. For example, brilliance refers to the ability of a the crown capture light and facets in the pavilion reflect stone to redirect light to the eyes of an observer so that the light by total internal reflection. This light capturing and gem’s crown appears illuminated. The effect of fire refers redirection function makes a gem appear illuminated and to the rainbow-like colors with which light exits a gem’s there are several illumination effects produced that make a facet as seen by an observer. Fire occurs because white stone appealing. The main illumination effects are bril- light entering or exiting a stone is dispersed into its con- liance, fire, and scintillation. There is a limited set of cuts stituent colors. The effect of scintillation refers to flashes of that favor the simultaneous presence of these effects that light, white or colored light, that are produced when the produce what is known in the trade as the life of a gem- gem, the observer, or the illumination source move. Scin- stone. Defining and quantifying brilliance, fire, and scintil- tillation is a dynamic and rich effect. The effect of leakage lation is relevant in the gem cutting industry where gem refers to light that exits the stone through the gem pavilion grading schemes are important for establishing value to rather than through the crown and may not contribute posi- gemstones and for informing the consumer. tively to the gemstone appeal. When a beam of light enters a gemstone it is split and A primary goal in gem cutting is to maximize the carat partitioned by the stone facets into a plurality of beams that weight of a given stone to be cut; however, recently there are totally internally reflected and then refracted out of the has been an emphasis in also maximizing the illumination stone. The refracted beams, through Fresnel splitting, create appeal of gems. The illumination effects produced by gems second and higher-order generations of beams that in turn have been traditionally evaluated with the unaided eye and with the aid of magnifiers. The first device to be recognized 0091-3286/2007/$25.00 © 2007 SPIE as an effective tool to aid in the cutting of stones is the Optical Engineering 093604-1 September 2007/Vol. 46͑9͒ Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones Fig. 3 Nomenclature to indicate ray directions. Normal to the gem table ͑the axis of the gem͒ is 90 deg and parallel to the table is 0 deg. about gemstone symmetry and brilliance, and the Angular Spectrum Evaluation Tool ͑ASET͒4 device, designed to show critical directions from which a gem captures light. Previous studies1,5–8 have been fruitful in understanding illumination effects in gemstones but have been limited in scope due to the lack of computing power. The develop- ment of nonsequential ray tracing software, commercial and company-proprietary, along with the ability to repre- Fig. 1 Nomenclature of the round brilliant cut. sent digitally and in detail the geometry of a given gem- stone has resulted in the ability to model and evaluate gem- stones with significant realism. For example, it is possible 9 ® 2 to design gems in a computer ͑GemCad ͒, model their ap- FireScope , which was invented in Japan in 1984 and de- ͑ 10͒ signed to judge brilliancy of precious stones. It is a simple pearance under different lighting conditions DiamCalc , and trace rays to extract other useful information ͑ASAP,11 device that uses a small cap painted internally red, a dif- 12 13 14 15͒ fused white light source, and 10X eyepiece. Other devices Fred, LightTools, TracePro, and ZEMAX . Given for gemstone evaluation have been invented such as the the ability for modeling gems in a computer there have Gilbertson3 instrument, designed to provide information been some interesting and useful studies of the round bril- liant diamond as performed by the Gemological Institute of America16,17 and Moscow State University.18,19 Recently there has also been progress in understanding the illumina- Fig. 4 Angular spectrum of a round brilliant as projected in the hemisphere. Each dot represents a ray direction that can make a Fig. 2 Light rays can enter the gem and be redirected to the eye virtual facet appear illuminated. Several ray refractions, including from different directions. the primary, are included. Optical Engineering 093604-2 September 2007/Vol. 46͑9͒ Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones Fig. 7 ͑a͒ Cut facets, ͑b͒ virtual facets upon the primary refraction as projected on the crown in the face-up position, and ͑c͒ virtual facets upon the primary and secondary refraction in the face-up position. 2 Gemstone Nomenclature Fig. 5 Angular spectrum of a round brilliant as projected in the In the jewelry industry there is a terminology to designate hemisphere. Only the primary refraction is displayed. different portions or regions of a given gemstone and for the purpose of this paper it is appropriate to review the 4,20–22 most significant entities as they pertain to the geometry of a tion effects in gemstones, in improving the cutting of gemstone. A gemstone is divided into regions comprising stones to exacting dimensions, and in development of better 23,24 flat surfaces called facets as shown in Fig. 1 in cross section tools for gem cut metrology. for the round brilliant diamond. The crown is the top por- In view of this progress, there is a renewed interest in tion of the stone, which in turn is divided into the table and the gemstone industry for grading gems based on their per- the bezel. The bezel contains the eight star facets, eight kite formance ͑illumination attributes͒ rather than in cut propor- facets, and sixteen upper girdle facets. The pavilion is the tions as has primarily been done for many decades. A grad- lower portion of the stone and is divided into the lower ing scheme based on illumination performance requires girdle facets, the pavilion main facets, and the culet. The characterization approaches that can quantify the light han- girdle separates the crown and the pavilion and comprises a dling abilities of gems. The American Gem Society has plurality of significantly smaller facets that are parallel to been engaged in producing a simple, consistent, and realis- the main axis of the stone. The axis of the stone passes tic approach to the optical testing and characterization of through the center of the culet and it is perpendicular to the gemstones, which is the subject of this paper. The primary table. For the case of the standard round brilliant cut dia- goals of this study are to define and evaluate the illumina- mond there are 58 facets, 33 in the crown and 25 in the tion attributes in gems of brilliance, fire, and scintillation.